1. Field
Certain aspects of the present disclosure generally relate to constant envelope spread-spectrum coding and, more particularly, to a method for demodulating a continuous phase modulated (CPM) signal.
2. Background
Spread-spectrum coding is a technique by which signals generated in a particular bandwidth can be spread in a frequency domain, resulting in a signal with a wider bandwidth. The spread signal has a lower power density, but the same total power as an un-spread signal. The expanded transmission bandwidth minimizes interference to others transmissions because of its low power density. At the receiver, the spread signal can be decoded, and the decoding operation provides resistance to interference and multipath fading.
Spread-spectrum coding is used in standardized systems, e.g. GSM, General Packet Radio Service (GPRS), Enhanced Digital GSM Evolution (EDGE), Code Division Multiple Access (CDMA), Wideband Code Division Multiple Access (WCDMA or W-CDMA), Orthogonal Frequency Division Multiplexing (OFDM), Orthogonal Frequency Division Multiple Access (OFDMA), Time Division Multiple Access (TDMA), Digital European Cordless Telecommunication (DECT), Infrared (IR), Wireless Fidelity (Wi-Fi), Bluetooth, Zigbee, Global Positioning System (GPS), Millimeter Wave (mmWave), Ultra Wideband (UWB), other standardized as well as non-standardized systems, wireless and wired communication systems.
In order to achieve good spreading characteristics in a system using spread spectrum, it is desirable to employ spreading codes which possess a near perfect periodic or aperiodic autocorrelation function, i.e. low sidelobes level as compared to the main peak, and an efficient correlator-matched filter to ease the processing at the receiver side. Spreading codes with high peak and low sidelobes level yields better acquisition and synchronization properties for communications, radar, and positioning applications.
In spread spectrum systems using multiple spreading codes, it is not sufficient to employ codes with good autocorrelation properties since such systems may suffer from multiple-access interference (MAI) and possibly inter-symbol interference (ISI). In order to achieve good spreading characteristics in a multi code DS-CDMA system, it is necessary to employ sequences having good autocorrelation properties as well as low cross-correlations. The cross-correlation between any two codes should be low to reduce MAI and ISI.
Complementary codes, first introduced by Golay in M. Golay, “Complementary Series,” IRE Transaction on Information Theory, Vol. 7, Issue 2, April 1961, are sets of complementary pairs of equally long, finite sequences of two kinds of elements which have the property that the number of pairs of like elements with any one given separation in one code is equal to the number of unlike elements with the same given separation in the other code. The complementary codes first discussed by Golay were pairs of binary complementary codes with elements +1 and −1 where the sum of their respective aperiodic autocorrelation sequence is zero everywhere, except for the center tap.
Polyphase complementary codes described in R. Sivaswamy, “Multiphase Complementary Codes,” IEEE Transaction on Information Theory, Vol. 24, Issue 5, September 1978, are codes where each element is a complex number with unit magnitude.
An efficient Golay correlator-matched filter was introduced by S. Budisin, “Efficient Pulse Compressor for Golay Complementary Sequences,” Electronic Letters, Vol. 27, Issue 3, January 1991, along with a recursive algorithm to generate these sequences as described in S. Budisin “New Complementary Pairs of Sequences,” Electronic Letters, Vol. 26, Issue 13, June 1990, and in S. Budisin “New Multilevel Complementary Pairs of Sequences,” Electronic Letters, Vol. 26, Issue 22, October 1990. The Golay complementary sequences described by Budisin are the most practical, they have lengths that are power of two, binary or complex, 2 levels or multi-levels, have good periodic and aperiodic autocorrelation functions and most importantly possess a highly efficient correlator-matched filter receiver.
However, Golay sequences are not without drawbacks. First, Golay sequences don't exist for every length, for example binary complementary Golay sequences are known for lengths 2M as well as for some even lengths that can be expressed as sum of two squares. Second, an efficient Golay correlator-matched filter exists only for Golay sequences generated by Budisin's recursive algorithm and that are of length that is a power of two (i.e. 2M). Third, the Golay sequences generated using Budisin's recursive algorithm might not possess the desired correlation properties. Furthermore, good spreading sequences such as m-sequences, Gold sequences, Barker sequences and other known sequences do not possess a highly efficient correlator-matched/mismatched filter.
WBAN (Wireless Body Area Networks) are envisioned to be crystal-less or will use cheap crystal oscillators. In both cases the system with have high ppm (parts per million) precision on the output frequency. For WBAN spread spectrum systems where there is a substantial frequency offset between the transmitter and the receiver, it might be advantageous to process the received signal differentially first. Golay sequences, m-sequences and other codes do not possess good correlation properties when detected differentially.
Finally, for low power applications such as wearable devices and wireless implants, there is a need for very low power radio that allows operation for long time before changing or charging the battery.
Therefore, there is a need in the art for a method of spread spectrum coding applied at the transmitter and an efficient method for de-spreading at the receiver that allows for large frequency drift between two communicating stations and for a method to reduce the power consumption at the receiver.
Furthermore, there is a need in the art for a practical constant envelope or quasi-constant envelope modulations that enable long battery life while still allowing practical encoding at the transmitter and practical decoding at the receiver.
A decomposition of binary CPM (Continuous Phase Modulation) as a sum of a finite number of time limited amplitude modulated pulse (AMP) was introduced by P. Laurent, “Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP),” IEEE Transaction on Communications, Vol. Com-34, No. 2, February 1982. This was later generalized to non-binary CPM by U. Mengali & al., “Decomposition of M-ary CPM Signals into PAM waveforms,” Vol. 41, No. 5, September 1995. In both cases, the number of pulses remained large for practical CPM modulations. Therefore, there is a need in the art for a single pulse representation of CPM signals which allow us to process CPM as a linear modulation in a similar fashion to BPSK, QPSK and QAM modulations.